The heat extraction from and cooling of computer microprocessors are challenging tasks in the modern era. Previously, the microprocessors were usually cooled by air, but now industry is shifting towards using nanofluids, as their properties are more thermo-physically stable. The experimental and numerical studies have revealed that the rate of heat transfer depends both on the thermal characteristics of the coolant and the geometry of the heat sink. For optimized results, it is recommended to analyze the combined effect of nanofluids and the geometry of the heat sink. Mini-channel heat sinks in combination with a nanofluid offered an excellent rate of heat transfer. However, passing nanofluids continuously through the system causes various problems over time; for example, the thermal stresses on the components are increased, which may lead to wear and tear of the system. In this study, a numerical investigation of mini-channel heat sinks was conducted through thermal-FSI. A numerical model was established with airfoil and Savonius pin-fin mini channel heat sinks, and they were analyzed at different flow rates from 0.25 LPM to 0.75 LPM with an increment of 0.25 LPM with different fluids, i.e., water, Al2O3–H2O, and Fe2O3–H2O nanofluids, varying their volumetric concentration. The minimum stresses were obtained while increasing the temperature drop and decreasing the pressure drop. The thermal stresses were calculated using the thermal-FSI technique and were found to be in the threshold range, and hence the material was within the yield limit at 0.75 LPM when using the Fe2O3-H2O Nanofluid at a 0° angle using the Savonius heat sink.